The present invention relates to a scanning optical element for a scanning optical system, and a scanning optical system employing the scanning optical element. The scanning optical element is used for converging a scanning beam on a surface to be scanned.
A conventional scanning optical system is configured such that a laser beam emitted by a laser diode is deflected by a polygonal mirror to scan within a predetermined angular range, and the scanning beam is converged on a surface to be scanned through a scanning optical system so that a beam spot is formed on the surface. The beam spot moves on the surface, as the polygonal mirror rotates, in a predetermined direction, which will be referred to hereinafter as a main scanning direction. The surface to be scanned is typically formed with a photosensitive layer, and by ON/OFF modulating the scanning laser beam, an electrostatic latent image can be formed on the surface.
In the description hereinafter, as defined above, a direction on the surface in which the beam spot moves is referred to as the main scanning direction, and a direction, on the surface, perpendicular to the main scanning direction is referred to as an auxiliary scanning direction. The shape and power of optical elements will also be explained with reference to the main and auxiliary scanning directions on the surface to be scanned.
In the scanning optical system, it is necessary that various aberrations on the surface to be scanned are well compensated for in accordance with a required accuracy of an image to be formed on the surface. Typically, in order to compensate for the aberrations, a plurality of anamorphic lenses are employed, or curved mirrors and an anamorphic lens are used in combination.
As described above, in the conventional scanning optical system, a plurality of lenses and/or mirror should be employed to compensate for the aberrations. Such a configuration make it difficult to reduce the size of the scanning optical system and/or manufacturing cost.
It is therefore an object of the present invention to provide an improved scanning optical element which is capable of compensating for the aberrations sufficiently and enables downsizing of the scanning optical system and lowering of the manufacturing cost.
For the object, according to an aspect of the invention, there is provided a scanning optical element for receiving a scanning light beam deflected to scan by a deflecting system and converging the received scanning light beam on a surface to be scanned such that a beam spot moving in a main scanning direction is formed on the surface to be scanned.
The scanning optical element is made of light transmitting material, and has a first surface that allows the received scanning light beam to pass through so that the scanning light beam proceeds in said scanning optical element, and a second surface that reflects the scanning beam proceeded in said scanning optical element and directs the scanning beam toward said first surface.
The first surface has a first intersection point with a first reference plane, and the second surface has a second intersection point with a second reference plane. The first reference plane and the second reference plane are perpendicular to a predetermined single axis. The first and second intersection points are on the reference axis, and the first surface is an optical curved surface which is tangent to the first reference plane at the first intersection point. The second surface being expressed by a SAG amount defined by a two-dimensional polynomial having variables which are two-dimensional coordinates, in the main scanning direction and in the auxiliary scanning direction, on the second reference plane. An origin point of the two-dimensional coordinates on the second reference plane is the second intersection point.
Coefficients for the two-dimensional polynomial defining the second surface being configured such that, a coefficient for a term having only a first order component with respect to the coordinates in the auxiliary scanning direction has a value other than zero.
Accordingly, the scanning optical element receives a light beam with a first surface, and reflects the beam with the second surface, the reflected beam emerging from the first surface. Therefore, the scanning optical element functions as an optical element having three surfaces. By shaping each surface appropriately, various aberrations can be well compensated for with a single optical element.
Optionally, each of the first surface and the second surface is a rotationally asymmetrical aspherical surface.
Further optionally, the first surface is symmetrical either in the main scanning direction and in the auxiliary scanning direction with respect to the origin point where the predetermined reference axis intersects with the first surface.
In the above case, coefficients of the polynomial expressing the second surface for odd order terms in the main scanning direction are zero.
Further optionally, the second surface may be expressed by a two-dimensional polynomial below,       X    ⁡          (              Y        ,        Z            )        =                              Y          2                +                  Z          2                            r        ⁢                  {                      1            +                                          1                -                                                                            (                                              κ                        +                        1                                            )                                        ⁢                                          (                                                                        Y                          2                                                +                                                  Z                          2                                                                    )                                                                            r                    2                                                                                }                      +          ∑              xe2x80x83            ⁢                        B          mn                ⁢                  Y          m                ⁢                  Z          n                    
where,
Y represents a height in the main scanning direction,
Z represents a height in the auxiliary scanning direction,
X(Y, Z) represents a SAG amount at a point (Y, Z) on the second reference plane,
r is a radius of curvature of the second surface on the origin point,
xcexa is a conical coefficient,
Bmn represent coefficients, and
a coefficient B01 has a value other than zero.
According to another aspect of the invention, there is provided a scanning optical system, which includes a light source, a polygonal mirror that is rotated to deflect a beam emitted by the light source to scan, and a scanning optical element for receiving a scanning light beam deflected to scan by a polygonal mirror and converging the received scanning light beam on a surface to be scanned such that a beam spot moving in a main scanning direction is formed on the surface to be scanned. Specifically, the scanning optical element is made of light transmitting material, and a first surface that allows the received scanning light beam to pass through so that the scanning light beam proceeds in the scanning optical element, and a second surface that reflects the scanning beam proceeded in the scanning optical element and directs the scanning beam toward the first surface.
The first surface has a first intersection point with a first reference plane, and the second surface has a second intersection point with a second reference plane. The first reference plane and the second reference plane are perpendicular to a predetermined single axis. The first and second intersection points are on the reference axis, and the first surface is an optical curved surface which is tangent to the first reference plane at the first intersection point. The second surface being expressed by a SAG amount defined by a two-dimensional polynomial having variables which are two-dimensional coordinates, in the main scanning direction and in the auxiliary scanning direction, on the second reference plane. An origin point of the two-dimensional coordinates on the second reference plane is the second intersection point.
Coefficients for the two-dimensional polynomial defining the second surface being configured such that, a coefficient for a term having only a first order component with respect to the coordinates in the auxiliary scanning direction has a value other than zero.
Optionally, the polygonal mirror and the scanning optical element being arranged such that a beam incident on the polygonal mirror and a beam reflected by the polygonal mirror are spatially separated in the auxiliary scanning direction, and a beam incident on the scanning optical element and a beam emerging from the scanning optical element are spatially separated in the auxiliary scanning direction.